Question

A cylindrical wire of radius r is carrying a current i uniformly distributed over its cross section if a circular loop of radius r is taken as amperian loop then the variation of value of £b.dl over this loop with radius r is

Answer 1

if the radius of the loop is taken inside the wire then enclosed current will be given by

$i_{net} = \frac{i}{\pia^2}{\pi r^2}$

$i_{net} = \frac{i r^2}{a^2}$

now by ampere's law we have

$\int B.dl = \mu_0 * \frac{i r^2}{a^2}$

so the integral will directly depends on the square of the radius

now when the loop is of bigger radius

$\int B.dl = \mu_0 i$

so outside it will be constant and not depends on the radius